Where does Blender store log information?
The paths for the crash logs are platform dependent. The following information can also be found in Blender's manual.
If you intend to add these information to a bug report, please attach the logs as file.
Windows
On Windows the location is determined by the environment variable TEMP. If you haven't modified this environment variable, it will point to C:\Users\[your username]\AppData\Local\Temp\. In order to locate the crash log, open the Windows Explorer (Win+E) and type %TEMP% into the path bar. The name of the crash log be the same as your project file, but with the file extension .crash.txt. If you haven't previously saved the project before, it will be blender.crash.txt.
Linux
On Linux the crash log is written to the /tmp directory. The name of the crash log be the same as your project file, but with the file extension .crash.txt. If you haven't previously saved the project before, it will be blender.crash.txt.
macOS
The crash log will be presented through the macOS Crash Reporter. You will have to copy the text and save it in a file yourself.

Additional information can be retrieved by starting Blender with debug command line flags.
Windows
The Windows version provides batch files for convenience that allow to create log files without using the command line. They are located in the same directory as the blender.exe.

blender_debug_gpu.cmd (--debug and --debug-gpu flags)
blender_debug_gpu_glitchworkaround(--debug, --debug-gpu and --debug-gpu-force-workarounds flags)
blender_debug_log.cmd (--debug and --debug-cycles flags)
blender_factory_startup.cmd (--factory-startup flag)

Double-clicking on the batch script will start Blender with the listed debug flags and write log files to %TEMP%\blender\debug_logs. Once Blender has either crashed or was manually closed, the Windows Explorer should automatically open and display the log files. If Blender was able to start, then this will also include a file that contains the system information blender_system_info.txt.
Linux
The log file creation requires to redirect stderr and stdout into a file. Open a terminal, navigate to the directory where Blender's binary is located and then use the following command or a variation with different command line flags:
./blender --debug --debug-cycles &gt; ~/blender_debug_output.txt 2&gt;&amp;1

The resulting log file will be placed in your home directory, assuming that your terminal supports the alias ~ for it.
macOS
The log file creation requires to redirect stderr and stdout into a file. Open a terminal and then use the following command or a variation with different command line flags
/Applications/Blender.app/Contents/MacOS/Blender --debug --debug-cycles &gt; ~/blender_debug_output.txt 2&gt;&amp;1

The resulting log file will be placed in your home directory.

Blender's command line also allows to configure additional logging options for more fine grained reporting.